已知xinα-sinβ=-1／3,cosα-cosβ=1／2,求cos(α-β)的值

Question

已知xinα-sinβ=-1／3 ,cosα-cosβ=1／2,求cos(α-β)的值

Answer 1

(sinα-sinβ)^2=(sinα)^2-2sinαsinβ+(sinβ)^2=1/9
(cosα-cosβ)^2=(cosα)^2-2cosαcosβ+(cosβ)^2=1/4
cos(α-β)=cosαcosβ+sinαsinβ=[-(sinα-sinβ)^2-(cosα-cosβ)^2+(sinα)^2+(sinβ)^2+(cosα)^2+(cosβ)^2]/2=[-1/9-1/4+1+1]/2=59/72